.TH std::log(std::complex) 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::log(std::complex) \- std::log(std::complex)

.SH Synopsis
   Defined in header <complex>
   template< class T >
   std::complex<T> log( const std::complex<T>& z );

   Computes complex natural (base e) logarithm of a complex value z with a branch cut
   along the negative real axis.

.SH Parameters

   z - complex value

.SH Return value

   If no errors occur, the complex natural logarithm of z is returned, in the range of
   a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically
   unbounded along the real axis.

   Error handling and special values

   Errors are reported consistent with math_errhandling.

   If the implementation supports IEEE floating-point arithmetic,

     * The function is continuous onto the branch cut taking into account the sign of
       imaginary part
     * std::log(std::conj(z)) == std::conj(std::log(z))
     * If z is (-0,+0), the result is (-∞,π) and FE_DIVBYZERO is raised
     * If z is (+0,+0), the result is (-∞,+0) and FE_DIVBYZERO is raised
     * If z is (x,+∞) (for any finite x), the result is (+∞,π/2)
     * If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may
       be raised
     * If z is (-∞,y) (for any finite positive y), the result is (+∞,π)
     * If z is (+∞,y) (for any finite positive y), the result is (+∞,+0)
     * If z is (-∞,+∞), the result is (+∞,3π/4)
     * If z is (+∞,+∞), the result is (+∞,π/4)
     * If z is (±∞,NaN), the result is (+∞,NaN)
     * If z is (NaN,y) (for any finite y), the result is (NaN,NaN) and FE_INVALID may
       be raised
     * If z is (NaN,+∞), the result is (+∞,NaN)
     * If z is (NaN,NaN), the result is (NaN,NaN)

.SH Notes

   The natural logarithm of a complex number z with polar coordinate components (r,θ)
   equals ln r + i(θ+2nπ), with the principal value ln r + iθ.

   The semantics of this function are intended to be consistent with the C function
   clog.

.SH Example


// Run this code

 #include <cmath>
 #include <complex>
 #include <iostream>

 int main()
 {
     std::complex<double> z {0.0, 1.0}; // r = 1, θ = pi / 2
     std::cout << "2 * log" << z << " = " << 2.0 * std::log(z) << '\\n';

     std::complex<double> z2 {sqrt(2.0) / 2, sqrt(2.0) / 2}; // r = 1, θ = pi / 4
     std::cout << "4 * log" << z2 << " = " << 4.0 * std::log(z2) << '\\n';

     std::complex<double> z3 {-1.0, 0.0}; // r = 1, θ = pi
     std::cout << "log" << z3 << " = " << std::log(z3) << '\\n';
     std::complex<double> z4 {-1.0, -0.0}; // the other side of the cut
     std::cout << "log" << z4 << " (the other side of the cut) = " << std::log(z4) << '\\n';
 }

.SH Possible output:

 2 * log(0,1) = (0,3.14159)
 4 * log(0.707107,0.707107) = (0,3.14159)
 log(-1,0) = (0,3.14159)
 log(-1,-0) (the other side of the cut) = (0,-3.14159)

   Defect reports

   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.

      DR    Applied to           Behavior as published              Correct behavior
   LWG 2597 C++98      specification mishandles signed zero       erroneous requirement
                       imaginary parts                            removed

.SH See also

                       complex common logarithm with the branch cuts along the negative
   log10(std::complex) real axis
                       \fI(function template)\fP
   exp(std::complex)   complex base e exponential
                       \fI(function template)\fP
   log
   logf                computes natural (base e) logarithm (\\({\\small\\ln{x}}\\)ln(x))
   logl                \fI(function)\fP
   \fI(C++11)\fP
   \fI(C++11)\fP
   log(std::valarray)  applies the function std::log to each element of valarray
                       \fI(function template)\fP
   C documentation for
   clog
